Question

$\underset{x\to a}{lim}\frac{\cos x-\cos a}{\cot x-\cot a}$ is equal to

• A. $\frac{1}{2}{\sin }^{3}a$
• B. $\frac{1}{2}cose{c}^{3}a$
• C. ${\sin }^{3}a$
• D. $cose{c}^{3}a$

Answer 1

The correct option is C ${\sin }^{3}a$

$\underset{x\to a}{lim}\frac{\cos x-\cos a}{\cot x-\cot a}=\frac{\cos a-\cos a}{\cot a-\cot a}\frac{0}{0}$form

L Hospital

$=\underset{x\to a}{lim}\frac{-\sin x-0}{-{\csc }^{2}x-0}=\underset{x\to a}{lim}{\sin }^{3}x$

$={\sin }^{3}a$